CN102506761A - Method for measuring curvature radius of aspheric surface vertex by using laser tracker - Google Patents
Method for measuring curvature radius of aspheric surface vertex by using laser tracker Download PDFInfo
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Abstract
A method for measuring the curvature radius of a vertex of an aspheric surface by using a laser tracker belongs to the technical field of optical testing, and comprises the steps of obtaining an aspheric surface coordinate point by using the laser tracker according to a specific mode, and obtaining the curvature radius of the vertex of the aspheric surface by data processing and an optimized search algorithm. The invention provides a novel method for measuring the curvature radius of the vertex of the aspheric surface, which is suitable for the in-situ measurement of the curvature radius of the vertex of the aspheric surface in the manufacturing and processing process, and particularly has important application value for the measurement of the curvature of the vertex of the large-caliber aspheric surface.
Description
Technical field
The invention belongs to the optic test field, relate to a kind of measuring method of aspheric surface vertex curvature radius, especially be suitable for the online detection of aperture aspherical vertex curvature radius.
Background technology
The aspheric surface vertex curvature radius is one of major parameter of decision aspheric optical system image quality, and the accurate measurement of vertex curvature radius is to optical aspherical surface processing and be equipped with important directive significance.
In the processing of traditional aspherical optical element, technicians are installed additional through dial gauge or clock gauge and are surveyed ring and measure the aspheric surface vertex curvature radius, and this method is easier, but can only rough measure, and error is bigger, only uses in aspheric surface moulding and grinding initial stage.
Contact contourgraph method is the measuring method of the small-bore aspheric surface vertex curvature radius used always, at first utilizes the contact pick-up unit to record a collection of discrete data, handles the radius-of-curvature that obtains institute's measuring wheel profile through appropriate data then.This method can't only be measured to a certain cross section of minute surface unified measurement, needs accurate location and measurement size and measuring accuracy limited, can not realize on-position measure.
The three coordinate measuring machine method is the measuring method of at present more common aspheric surface vertex curvature radius, obtains unified measurement data through three-dimensional the moving of three-dimensional gauge head, and the method through least square fitting obtains vertex curvature radius.The three coordinate measuring machine method can realize higher measuring accuracy, small-bore aspheric measurement in satisfying.Its shortcoming is the restriction that still receives the three-dimensional coordinates measurement range of size, and the aspheric surface size needs before measuring to carry out the measurement point programming to measured piece less than 2 meters usually, can not realize on-position measure.
Summary of the invention
The technical matters that the present invention will solve: in order to overcome the deficiency that prior art exists, a kind of method of utilizing laser tracker to measure the aspheric surface vertex curvature radius is provided, has realized on-position measure.
Technical solution of the present invention: a kind of method of utilizing laser tracker to measure the aspheric surface vertex curvature radius, performing step is following:
Step S1 uses laser tracker to set up the non-spherical measuring coordinate system;
Step S2 uses laser tracker to gather the aspheric surface coordinate points;
Step S3 uses laser tracker to gather gained aspheric surface coordinate points and slightly builds the aspheric surface coordinate system, and the aspheric surface coordinate points is carried out coordinate transform;
Step S4 sets vertex curvature radius span and step-length, is parameter with span inner vertex radius-of-curvature value respectively, and the aspheric surface coordinate points is carried out the compensation of the target radius of a ball;
Step S5 carries out the aspheric surface match to each group compensation back aspheric surface coordinate points according to the vertex curvature radius value corresponding with radius compensation, and essence is built the aspheric surface coordinate system row-coordinate conversion of going forward side by side.Calculate the root-mean-square-deviation of coordinate points and corresponding aspheric surface fit equation after every group of coordinate conversion, the pairing vertex curvature radius value of lowest mean square root deviate is by being asked the aspheric surface vertex curvature radius.
Among the said step S2; Use laser tracker to gather the aspheric surface coordinate points according to radially adopting point mode, said radially adopt point mode be sampled point along the aspheric surface diameter Distribution, measurement point is identical at interval on the diameter; Diameter bar number should be more than or equal to 2, and angle equates between the diameter.
Among the said step S4; The method of the spherical co-ordinate point being carried out the compensation of the target radius of a ball is: through the aspheric surface coordinate points; In conjunction with the aspheric surface equation of selected vertex curvature radius target ball contact point coordinate approximate coordinates is calculated as parameter; Obtain the direction vector of contact point coordinate place aspheric surface equation, the service orientation vector carries out radius compensation to the coordinate points under the thick coordinate system.
The present invention's beneficial effect compared with prior art:
(1) with respect to traditional measurement method, the method that the present invention utilizes laser tracker to measure the aspheric surface vertex curvature radius is not limited by the aspheric surface bore, and measurement point need not programmed, and efficiency of measurement and precision are higher, can be implemented in line and measure, and measurement range is big;
(2) to measure the time spent few in the present invention, can promote aspheric detection efficiency, shortens and make the duration; Measuring accuracy is high; Can contain aspheric surface from of the detection of processing initial stage until finished product; Be a kind of agile and all-purpose measuring method, be applicable to the measurement of the vertex curvature radius of aspheric surface in processing and whole inspection, be particularly useful for the measurement of vertex curvature radius in the aperture aspherical process.
Description of drawings
Fig. 1 measures the process flow diagram of aspheric surface vertex curvature radius for the present invention utilizes laser tracker;
Fig. 2 sets up synoptic diagram for aspheric surface coordinate system of the present invention;
Fig. 3 radially adopts a synoptic diagram for the present invention;
Fig. 4 is that target ball and minute surface contact point calculate synoptic diagram.
Embodiment
Specify each detailed problem that relates in the technical scheme of the present invention below in conjunction with accompanying drawing.Be to be noted that described case study on implementation only is intended to be convenient to understanding of the present invention, and do not play any qualification effect.
(1) laser tracker that utilizes as shown in Figure 1 is measured the method flow diagram of aspheric surface vertex curvature radius; Should at first use laser tracker to set up the non-spherical measuring coordinate system; Measurement coordinate system should make the aspheric surface turning axle overlap with a certain coordinate axis, and the aspheric surface summit overlaps with the coordinate axis initial point.The foundation of non-spherical measuring coordinate system can be follow-up searching best-fit aspheric surface reasonable initial value is provided, and avoids calculating and makes mistakes.Setting up measurement coordinate system can realize through aspheric pattern measurement.As shown in Figure 2, use 3-2-1 mode commonly used to set up coordinate system, promptly measure and generate plane, aspheric surface upper surface, X-direction straight line, the aspheric surface cylindrical center of circle and set up the aspheric surface coordinate system.
(2) use laser tracker to gather the aspheric surface coordinate points according to radially adopting point mode, the radial distribution point can make sampled point balanced in the weight of aspheric surface Internal and external cycle, reduces the original reason error that follow-up fitting algorithm produces.Radially adopting point mode is that sampled point is along the aspheric surface diameter Distribution; Measurement point distributes roughly the same (not having strict status requirement) at interval on the diameter, and measuring diameter bar number should be more than or equal to 2, and angle equates between the diameter; Be illustrated in figure 3 as a kind of radial distribution synoptic diagram, measurement point is a rice word line radial distribution.Single adopts a time and average time can pass through the setting of laser tracker Survey Software.
(3) use laser tracker to gather the gained coordinate points and slightly build the aspheric surface coordinate system, the aspheric surface coordinate points is carried out coordinate transform.Slightly build coordinate system and can a coordinate system benchmark accurately be provided for the compensation of the target radius of a ball.Slightly building coordinate system implements as follows: with (R-r) is that (wherein R is the design vertex curvature radius to aspheric surface vertex curvature parameter; R is the target radius of a ball); Calculate inclination, translational movement that respective coordinates system of match aspheric surface institute and measurement coordinate system exist, and the point under the converted measurement coordinate system is to slightly building under the coordinate system.Wherein calculate the match aspheric surface and be equal to multiparameter and do not have the constraint nonlinear optimal problem, suc as formula:
F (Δ x, Δ y, Δ z, Δ α, Δ β)=∑ (z
Ai-f (x
Ai, y
Ai))
2, wherein, x
a, y
a, z
aBe the corresponding down coordinate of match aspheric surface coordinate system, f (x
a, y
a) be the aspheric surface functional relation, can use the Matlab optimization tool to find the solution D translation amount Δ x, Δ y, Δ z, relative Z axle tilt quantity Δ α, Δ β makes the objective function F value reach minimum.Coordinate transformation suc as formula:
Wherein, x
m, y
m, z
mBe three-dimensional coordinate under the measurement coordinate system.
(4) because the aspheric surface vertex curvature radius is unknown, the aspheric surface parameter of the required usefulness of radius compensation can not be provided accurately.For this problem, solution is following: setting vertex curvature radius span and step-length, is parameter with span inner vertex radius-of-curvature value respectively, and the aspheric surface coordinate points is carried out the compensation of the target radius of a ball, carries out optimum through follow-up method and judges.Wherein the radius-of-curvature step-length is set with measuring accuracy and is required (1/3-1/10), and scope is an aspheric surface vertex curvature mismachining tolerance.As shown in Figure 4, calculate contact point approximate direction vector according to selected vertex curvature radius value and target ball center coordinate figure, calculate the contact point coordinate position according to the use target radius of a ball, suc as formula:
Next calculates the accurate direction vector of contact point:
(5) target radius of a ball compensation back data are carried out the aspheric surface match according to the radius-of-curvature of corresponding (compensating used) respectively, essence is built the aspheric surface coordinate system, the row-coordinate of going forward side by side conversion (slightly building aspheric surface coordinate system and coordinate transformation method in method such as the step 3).Calculate the root-mean-square-deviation of each group data and corresponding aspheric surface fit equation, the vertex curvature radius of getting the minimum set of coordinates correspondence of root-mean-square-deviation is the aspheric surface vertex curvature radius.Wherein the root-mean-square-deviation computing method are:
Wherein, rms is a root-mean-square-deviation, x
Ji, y
Ji, z
JiFor essence is built the coordinate points under the aspheric surface coordinate system, f (x
Ji, y
Ji, R
k) be with R
kBe the aspheric surface equation of parameter, n is a measure dot number, R
kBe the used vertex curvature radius of respective radii compensation.The optimal curvature radius R
aMake rms
a=min (rms
j).
The present invention does not set forth in detail and belongs to techniques well known.
Claims (3)
1. method of utilizing laser tracker to measure the aspheric surface vertex curvature radius is characterized in that performing step is following:
Step S1 uses laser tracker to set up the non-spherical measuring coordinate system;
Step S2 uses laser tracker to gather the aspheric surface coordinate points;
Step S3 uses laser tracker to gather gained aspheric surface coordinate points and slightly builds the aspheric surface coordinate system, and the aspheric surface coordinate points is carried out coordinate transform;
Step S4 sets vertex curvature radius span and step-length, is parameter with span inner vertex radius-of-curvature value respectively, and the aspheric surface coordinate points is carried out the compensation of the target radius of a ball;
Step S5; Each group compensation back aspheric surface coordinate points is carried out the aspheric surface match according to the vertex curvature radius value corresponding with radius compensation; Essence is built the go forward side by side row-coordinate conversion of aspheric surface coordinate system; Calculate the root-mean-square-deviation of coordinate points and corresponding aspheric surface fit equation after every group of coordinate conversion, the pairing vertex curvature radius value of lowest mean square root deviate is by being asked the aspheric surface vertex curvature radius.
2. according to right 1 described a kind of method of utilizing laser tracker to measure the aspheric surface vertex curvature radius; It is characterized in that: among the said step S2; Use laser tracker to gather the aspheric surface coordinate points according to radially adopting point mode, said radially adopt point mode be sampled point along the aspheric surface diameter Distribution, measurement point is identical at interval on the diameter; Diameter bar number should be more than or equal to 2, and angle equates between the diameter.
3. according to right 1 described a kind of method of utilizing laser tracker to measure the aspheric surface vertex curvature radius; It is characterized in that: among the said step S4; The method of the spherical co-ordinate point being carried out the compensation of the target radius of a ball is: through the aspheric surface coordinate points; In conjunction with the aspheric surface equation of selected vertex curvature radius target ball contact point coordinate approximate coordinates is calculated as parameter; Obtain the direction vector of contact point coordinate place aspheric surface equation, the service orientation vector carries out radius compensation to the coordinate points under the thick coordinate system.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103926058A (en) * | 2014-03-27 | 2014-07-16 | 中国科学院长春光学精密机械与物理研究所 | Method for measuring optical axis in aspheric surface detection by means of self-aligning plane mirror |
| CN104596420A (en) * | 2015-01-26 | 2015-05-06 | 北京卫星环境工程研究所 | Accurate measurement method for measuring benchmark cubic mirror central point position with laser tracker |
| CN105698709A (en) * | 2016-03-24 | 2016-06-22 | 洛阳亨基智能数控装备科技有限公司 | Measurement method for curvature radius of tapered roller |
| CN106871819A (en) * | 2017-01-12 | 2017-06-20 | 北京理工大学 | Aspherical vertex curvature radius error measurement method based on the optimal compensation position |
| CN107918178A (en) * | 2017-12-14 | 2018-04-17 | 中国航空工业集团公司洛阳电光设备研究所 | The method that one kind improves the aspherical glued precision of 100mm ~ 150mm bores |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103926058A (en) * | 2014-03-27 | 2014-07-16 | 中国科学院长春光学精密机械与物理研究所 | Method for measuring optical axis in aspheric surface detection by means of self-aligning plane mirror |
| CN103926058B (en) * | 2014-03-27 | 2016-08-17 | 中国科学院长春光学精密机械与物理研究所 | The method using autocollimatic plane mirror measurement optical axis in Aspherical-surface testing |
| CN104596420A (en) * | 2015-01-26 | 2015-05-06 | 北京卫星环境工程研究所 | Accurate measurement method for measuring benchmark cubic mirror central point position with laser tracker |
| CN104596420B (en) * | 2015-01-26 | 2017-06-16 | 北京卫星环境工程研究所 | The accurate measurement method of laser tracker measuring basis prism square center position |
| CN105698709A (en) * | 2016-03-24 | 2016-06-22 | 洛阳亨基智能数控装备科技有限公司 | Measurement method for curvature radius of tapered roller |
| CN105698709B (en) * | 2016-03-24 | 2018-02-09 | 洛阳亨基智能数控装备科技有限公司 | A kind of measuring method of taper roller radius of curvature |
| CN106871819A (en) * | 2017-01-12 | 2017-06-20 | 北京理工大学 | Aspherical vertex curvature radius error measurement method based on the optimal compensation position |
| CN106871819B (en) * | 2017-01-12 | 2019-03-26 | 北京理工大学 | Aspherical vertex curvature radius error measurement method based on the optimal compensation position |
| CN107918178A (en) * | 2017-12-14 | 2018-04-17 | 中国航空工业集团公司洛阳电光设备研究所 | The method that one kind improves the aspherical glued precision of 100mm ~ 150mm bores |
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